Issue 64

P. Ghannadi et alii, Frattura ed Integrità Strutturale, 64 (2023) 51-76; DOI: 10.3221/IGF-ESIS.64.04

procedure for civil infrastructures and structures [6]. In 2007, I35W Bridge (Mississippi, Minneapolis, USA) collapsed. Unfortunately, 13 died, and also 145 were injured. In addition, significant financial losses were imposed. This incident and similar ones could be prevented by implementing suitable SHM systems and detecting damages at their early stages [7]. Structural damage detection is the central part of SHM systems, consisting of automatic procedures for identifying and quantifying existing damages. The schematic of this process is briefly illustrated in Fig. 1. Typical damage detection strategies include three phases. In the first phase, several accelerometers measure acceleration responses. In the second phase, data acquisition systems are employed to collect data. The measured data are processed in the third phase through different damage detection and quantification algorithms [8]. It should be noted that the acceleration signals for a large-scale structure such as Milad Tower (shown in Fig. 1) are usually measured under ambient excitation [9]. Local stiffness decreases due to structural damage [10]. This stiffness loss is reflected in dynamic characteristics such as natural frequencies and mode shapes. The variation of dynamic characteristics before the damage occurrence and damaged state can be analyzed through vibration-based damage identification methodologies for detecting the damage and quantifying its extent [11]. Vibration-based methods are classified into two divisions: I) Response-based methods II) Model-based methods. Response-based methods are usually categorized as nonparametric approaches, and there is no need for finite element simulation as a baseline model. These methods typically require experimental response data and can only detect damaged elements. Response-based methods are a proper selection to establish a real-time SHM system because of their low computational cost [12]. In this regard, several signal processing techniques based on wavelet transformation and Hilbert–Huang transform have been introduced to address the structural damage detection problem more sensitively [13–18]. Model-based methods can identify both location and severity of the damaged elements. Experimental measurements and FEM of the structures are required to put model-based approaches into practice [12]. The following difficulties arise while using these techniques: a. The numerical models should accurately represent the behavior of the structures. Therefore, developing a high-fidelity FEM of the complex structures takes considerable effort [19]. To perform a dynamic analysis [20] of Milad Tower (shown in Fig. 1), a reliable FEM is carried out by Strand7 software [21], which can be implemented in future damage detection methodologies. b. There are some differences between the experimental results and those obtained by FEM due to the uncertainties in boundary conditions, material properties, and geometry [22]. Therefore, FEM updating is implemented as a crucial procedure to meet a good agreement between the measured and calculated modal characteristics [23]. A survey of FEM updating techniques in structural dynamics was presented by Mottershead and Friswell [24]. Recently, in 2015, another review paper in the area of FEM updating was published [25]. A comparative study of existing FEM updating methods has been conducted by Arora [26]. c. In real-world SHM projects, the size of measured degrees of freedom (DOFs) does not match the full set of DOFs of the FEM [27] because measuring the mode shapes at all DOFs is not practical, and there is no economic justification for it. To overcome incomplete measurements, either FEM reduction or mode shape expansion methods can be utilized [28]. Ghannadi and Kourehli have investigated the efficiency of different FEM reduction techniques [29]. Dinh-Cong et al. presented a comparative study of different dynamic condensation methods in detecting damages in plate-like structures [30]. Some damage detection methodologies based on expansion techniques can be found in Refs. [31–34]. d. Using complex FEM such as Milad Tower (shown in Fig. 1) is not practical for structural damage detection because of the extensive computational workload [35]. Hence, some simplified models are typically developed to represent the dynamic behavior of the structures. The simplified models can significantly reduce the computation time [36]. To detect damages, predict seismic responses, and optimize sensor locations, the FEMs of some famous structures such as Guangzhou New TV Tower [37], Shanghai Tower [36,38], MIT Green Building [39,40], and Dalian World Trade Building [41] were simplified. Pourkamali-Anaraki and Hariri-Ardebili have presented a two-step uncertainty quantification method that uses a simplified alternative model of Milad Tower [42]. The classification of vibration-based damage detection methods is illustrated in Fig. 2. In the recent two decades, model-based structural damage identification through an iterative optimization process has received significant attention [12]. The earliest damage detection methods have been developed based on the genetic algorithm (GA) [43–45]. Dynamic characteristics such as natural frequencies and mode shapes are employed to construct an objective function when using optimization-based damage detection methods [12]. In recent years, some novel optimization algorithms have been rapidly developed. For instance, several researchers have employed moth-flame [46], salp swarm [47], multiverse [48], whale [49], YUKI [50,51], wild horse [52] and slime mold [53] algorithms to solve the inverse problem of damage detection. However, conventional optimization methods such as simulated annealing (SA), particle swarm optimization (PSO) [54], and GA are still often used in damage identification problems. During the last two decades, the application of the SA algorithm is not limited to damage detection problems but also has other functions in

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